2003 Reports

# On the uniqueness of convex-ranged probabilities

We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convex-ranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S, Σ), the condition [∃A∗ ∈ Σ with 0 < P(A∗) < 1 such that P(A∗) = P(B)=⇒ Q(A∗) = Q(B) whenever B∈Σ] is equivalent to the condition [∀A,B ∈ Σ P(A) > P(B)=⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q.

## Subjects

## Files

- econ_0203_24.pdf application/pdf 265 KB Download File

## More About This Work

- Academic Units
- Economics
- Publisher
- Department of Economics, Columbia University
- Series
- Department of Economics Discussion Papers, 0203-24
- Published Here
- March 24, 2011

## Notes

August 2003